Abstract: For a long time the classical expectation hypothesis has been challenged from both empirical and theoretical perspective. Still no one could explain entirely the existent bias between expected future spot rates and forward rates, the so called puzzle in the expectation hypothesis. In this work we will address this issue through arbitrage theory, in particular, focusing our attention in a connection of the classical expectation hypothesis to a certain probability measures where the relation between expected future spot rates and forward rates holds. We will approach this applying certain instantaneous spot rate models, verifying in these models that through changes from "real world" probability measure to other probability measures, we will find adjustments that will able us to explain this bias in the expectation hypothesis.